Euclidean Bus Mobility and Route Optimization, A Comparison

Routes in Queens, New York City, NY

Author

Alan Vlakancic

Published

November 30, 2025

Introduction

This project uses stplanr transport modeling package to design an optimal transport route for bus or cycle routes in New York City. Stplanr is a transport planning visualization R package that can be used to plan transit networks, in addition to transit planning elements such as identifying transit catchment areas, origin/destination data and ride frequency visualizations, among others. In their white paper, the devlopers of stplanr call for an accountable, transparent and democratized transit planning system that doesn’t rely on proprietary and often vastly different data sources and data processing softwares. Although the package can visualize a whole host of data, this project will focus on comparing direct desire lines or “Euclidean” routes (as the crow flies), existing bus networks and stplanr’s optimized routes. To wit: this can map the efficiency of the bus routes compared to the most direct route possible if there were no built environment factors in the way.

Methods

To adequately compare desire lines, bus routes, and the most efficient routes with the current street network, this project will require at minimum three data sources. Each of these will be sourced separately and overlaid onto each other:

  • Data Source: leaflet data for basemap
    • Methods: This can be sourced directly into R by installing the leaflet package. It provides an interactive background map that can be used to overlay other spatial data, and the options can be toggled on and off for ease of use.
    • Source: Leaflet for R
  • Data Source: OpenStreetMap (OSMR) data for transit data, either bus or cycle routes, this is used as the route vector data.
    • Methods: This can be sourced directly into R by installing the package. You may need to rationalize different projection systems to make sure they overlay correctly.
    • Source: Mapping with OpenStreetMap in R
  • Data Source: NYC Open Data for Bus Shelter locations
    Despite significant searching, there is no comprehensive bus stop dataset, so the project will focus on bus stop shelters, which are mapped via NYC Open Data. I used Bus Shelters as there would be thousands upon thousands of bus stops in NYC, and this would be too computationally intensive to process.
    • Methods: This can be brought into R as a CSV file. Each bus stop shelter has longitude and latitude coordinates that align with leaflet and OpenStreetMap projections.
    • Source: NYC Bus Stop Shelters, NYC Transit analysis
  • Data Source: NYC Open Data for NYC Borough Boundaries

Data Preparation

  • Load the necessary R packages for spatial data manipulation and visualization (e.g., ggmap, dplyr, stplanr, osmdata, sf, leaflet).
  • Import the NYC basemap shapefile and bus shelter CSV data into R.
  • Convert the bus shelter data into an sf object with appropriate coordinate reference system (CRS).

Terms:

  • Desire Lines: Straight lines connecting origin and destination points, representing the most direct path between them.
  • Euclidean: Direct points between shelters. “As the crow flies”.
  • OSRM: Open Street Routing Machine, a routing engine that uses Open Street Map data to calculate routes, shortest routes, travel times, and can be used to make travel time maps, distance routing for car, bike and walking.

Interactive Map:

Show code
library(ggmap)
library(dplyr)
library(stplanr)
library(osmdata)
library(sf)
library(tidyverse)
library(leaflet)
library(purrr)
library(kableExtra)
library(scales)

bbox <- c(left = -73.96, bottom = 40.54, right = -73.70, top = 40.81)
#create bounding box for NYC

nyc_map <- "data/"#

#nyc basemap, downloaded from nyc open data. source: https://search.r-project.org/CRAN/refmans/ptools/html/nyc_bor.html

nyc_sf <- st_read(nyc_map)
Reading layer `nybb' from data source 
  `C:\Users\vlakanah\OneDrive - Alfred State College\01. Semesters\14. 2025 FA\GEO511\GEO511_FinalProject\data' 
  using driver `ESRI Shapefile'
Simple feature collection with 5 features and 4 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 913175.1 ymin: 120121.9 xmax: 1067383 ymax: 272844.3
Projected CRS: NAD83 / New York Long Island (ftUS)
Show code
#bring in nyc_map as a sf

shelters_sf <- read_csv("data/Bus_Stop_Shelter_20251020.csv")
#NOTE: REPLACE WITH DATA WHEN USING QUARTO!
#this brings in the bus stop shelter information. source: https://data.cityofnewyork.us/Transportation/Bus-Stop-Shelters/qafz-7myz

shelters_sf_fix <- st_as_sf(shelters_sf, coords = c("Longitude","Latitude"), crs = 4326)
#convert to sf object with the correct coordinate reference system

osmdata::set_overpass_url("https://overpass-api.de/api/interpreter")
#set overpass url for open street maps

osm_data <- opq(bbox = bbox) %>%
  add_osm_feature(key = "highway", value = c("primary","secondary")) %>%
  osmdata_sf()
#import data for primary and secondary highways from open street maps

shelters_sf_fix <- shelters_sf_fix %>%
  mutate(id = paste0("S", row_number()))
#add ID column for origin-destination pairs so they have a corresponding number

flow_all <- expand.grid(o = shelters_sf_fix$id, #create origin
                        d = shelters_sf_fix$id, #create destination
                        stringsAsFactors = FALSE) %>% #make sure they aren't factors
  filter(o != d) %>% # this remove self-pairs so O is not D
  mutate(trips = 1) %>% #add trip count of 1 for each pair
  sample_n(50) #sample 50 random paris to avoid blowing up the computer

desire_lines_all <- od2line(flow_all, zones = shelters_sf_fix, zone_code = "id") #use od2line function to create desire lines (euclidean) for all pairs

shelter_coords <- shelters_sf_fix %>%
  st_coordinates() %>%
  as.data.frame() %>%
  bind_cols(id = shelters_sf_fix$id)
#extract coordinates and bind with ID column

route_single <- function(o_id, d_id) { #function to create a single route between origin and destination
  o <- shelter_coords %>% filter(id == o_id) 
  #filter to get origin coordinates
  d <- shelter_coords %>% filter(id == d_id)
  #filter to get destination coordinates

  r <- try(route_osrm(from = c(o$X, o$Y),
                      to   = c(d$X, d$Y)), silent = TRUE)
#use try to catch errors  (e.g., no route found)
  if (inherits(r, "try-error")) return(NULL)
#if route found, return the route
  return(r)
}

routes_list <- purrr::map2(flow_all$o, flow_all$d, route_single)
#create routes for all origin-destination pairs using the route_single function
routes_list <- routes_list[!sapply(routes_list, is.null)]
#remove any NULL results (failed routes)
routes_sf <- do.call(rbind, routes_list)
#combine all routes into a single sf object

#BELOW: create a comparison between route lengths and desire line lengths & calculate means and percent change

routes_projection <- st_transform(routes_sf, 32618)
desire_projection <- st_transform(desire_lines_all, 32618)
#ensures the correct, projected shapefile for computation not mapping

route_length <- st_length(routes_projection)
desire_length <- st_length(desire_projection)
#compute lengths

route_length <- as.numeric(route_length)
desire_length <- as.numeric(desire_length)
#convert lengths to numeric values

lengths_tbl <- tibble(
  route_m  = route_length,
  desire_m = desire_length,
  origin = flow_all$o,
  destination = flow_all$d
)
#create tibble to compare lengths in the final map w/ IDs

lengths_tbl_print <- tibble(
  route_m  = comma(round(route_length)),
  desire_m = comma(round(desire_length)),
  origin = flow_all$o,
  destination = flow_all$d
)
#tidy data for later printing in a kable

mean_route <- mean(route_length, na.rm = TRUE)
mean_desire <- mean(desire_length, na.rm = TRUE)
#calculate means for both route and desire lengths

percent_change <- ((mean_route - mean_desire) / mean_desire) * 100
#calculate percent change 

mean_lengths <- data.frame(
  type = c("Route Length", "Desire Line Length"),
  mean_length_m = c(round(mean_route), round(mean_desire)))

#put these into a data frame, rounded to whole numbers


mean_lengths <- mean_lengths %>%
  mutate(
    mean_length_km = mean_length_m / 1000,
    percent_change = c(percent_change, NA)
  )
#add km conversion and percent change to the data frame, i converted to KM for ease of computation (ie: dividing by 1,000)

mean_lengths_print <- mean_lengths %>%
  mutate(
    mean_length_km = comma(round(mean_length_m / 1000)),
    percent_change = comma(round(percent_change))
  )

nyc_leaflet  <- st_transform(nyc_sf, 4326)
roads_leaflet <- st_transform(osm_data$osm_lines, 4326)
desire_leaflet <- st_transform(desire_lines_all, 4326)
routes_leaflet <- st_transform(routes_sf, 4326)
#transform all data to WGS84 for leaflet mapping

desire_leaflet_popup <- paste0(
  "<b>Desire Line</b><br/>",
  "Origin: ", desire_leaflet$o, "<br/>",
  "Destination: ", desire_leaflet$d, "<br/>",
  "Desire Line Distance: ", round(lengths_tbl$desire_m / 1000), " km"
)
#create popup info for desire lines for interactive map
  
routes_leaflet_popup <- paste0(
  "<b>OSRM Route</b><br/>",
  "Origin: ", desire_leaflet$o, "<br/>",
  "Destination: ", desire_leaflet$d, "<br/>",
  "Route Distance: ", round(lengths_tbl$route_m / 1000), " km<br/>"
)
#create popup info for routes for interactive map

pal_desire <- colorNumeric(
  palette = "viridis",
  domain  = lengths_tbl$desire_m
)
#create color palette for desire lines based on distance

pal_routes <- colorNumeric(
  palette = "inferno",
  domain  = lengths_tbl$route_m
)
#create color palette for routes based on distance

selected_ids <- unique(c(flow_all$o, flow_all$d))
#get unique IDs of sampled shelters

selected_shelters <- shelters_sf_fix %>% 
  filter(id %in% selected_ids)
#filter shelters to only those that were sampled

leaflet() %>%
  addProviderTiles("CartoDB.Positron") %>%
  
  addPolygons(data = nyc_leaflet,
              color = "black", weight = 3,
              fillOpacity = 0.1,
              group = "NYC Boundary") %>%
  # Add OSM roads w/ positron background
  
  addPolylines(
    data = desire_leaflet,
    color = pal_desire(lengths_tbl$desire_m),
    weight = 3,
    opacity = 0.7,
    popup = desire_leaflet_popup,
    group = "Desire Lines"
  ) %>%
  
  addPolylines(
    data = routes_leaflet,
    color = pal_routes(lengths_tbl$route_m),
    weight = 3,
    opacity = 0.8,
    popup = routes_leaflet_popup,
    group = "OSRM Routes"
  ) %>%
  
  addLegend(
    pal = pal_desire,
    values = lengths_tbl$desire_m,
    title = "Desire Line Distance (m)",
    position = "bottomright",
    group = "Desire Lines"
  ) %>%
  #add a legend for desire lines
  addLegend(
    pal = pal_routes,
    values = lengths_tbl$route_m,
    title = "OSRM Route Distance (m)",
    position = "bottomleft",
    group = "OSRM Routes"
  ) %>%
  #add a legend for osrm routes

    addCircleMarkers(data = shelters_sf_fix,
                   color = "blue",
                   radius = 1,
                   popup = ~id,
                   group = "Bus Shelters") %>%
  #add all bus shelters
  addCircleMarkers(
    data = selected_shelters,
    color = "purple",
    radius = 6,
    fillOpacity = 0.9,
    group = "Sampled Shelters"
  ) %>%
  #add sampled bus shelters with purple markers
  addLayersControl(
    overlayGroups = c("NYC Boundary", "Sampled Shelters",
                      "Desire Lines", "OSRM Routes",
                      "Bus Shelters"),
    options = layersControlOptions(collapsed = FALSE)
  )

Tables:

Show code
mean_lengths_print %>%
  kable(col.names = c("Type", "Mean Length (m)", "Mean Length (km)", "Percent Change (%)"),
        caption = "Mean Lengths of OSRM Routes vs Desire Lines") %>%
  kable_styling(full_width = FALSE, position = "left")
Mean Lengths of OSRM Routes vs Desire Lines
Type Mean Length (m) Mean Length (km) Percent Change (%)
Route Length 17712 18 20
Desire Line Length 14736 15 NA
Show code
lengths_tbl_print %>%
  kable(col.names = c("Route Length (m)", "Desire Line Length (m)", "Origin ID", "Destination ID"),
        caption = "Comparison of Route Lengths and Desire Line Lengths for Sampled Origin-Destination Pairs") %>%
  kable_styling(full_width = FALSE, position = "left")
Comparison of Route Lengths and Desire Line Lengths for Sampled Origin-Destination Pairs
Route Length (m) Desire Line Length (m) Origin ID Destination ID
3,239 2,704 S1934 S1956
18,208 16,401 S279 S2557
17,575 15,004 S2594 S279
22,644 18,377 S3322 S357
6,621 5,706 S2050 S2062
27,109 12,630 S1432 S2515
28,281 23,475 S953 S2671
29,248 26,729 S2492 S826
11,193 9,890 S2157 S1417
15,280 11,642 S1045 S1649
25,838 18,839 S2459 S2414
14,862 13,688 S1318 S1734
7,680 6,599 S97 S1993
4,479 3,476 S1806 S1314
23,398 21,380 S3219 S2270
2,719 2,251 S685 S358
28,975 20,848 S1123 S3035
15,540 13,822 S34 S3095
13,917 12,144 S2099 S2874
15,012 11,603 S2595 S2163
29,646 19,728 S1228 S2500
20,924 18,431 S395 S2376
12,584 10,552 S2142 S451
12,721 11,506 S2315 S220
22,654 19,688 S1581 S802
16,681 14,683 S903 S2094
9,169 7,908 S1964 S176
20,550 18,946 S597 S2780
4,127 4,031 S702 S2977
6,889 6,196 S2323 S2112
14,295 11,974 S1747 S2281
18,219 15,615 S2195 S666
27,406 20,385 S2379 S1419
1,836 1,470 S2173 S1416
18,436 16,498 S866 S1860
36,554 33,209 S3221 S1550
17,991 15,371 S2143 S1418
26,754 23,599 S3339 S1496
36,112 31,710 S181 S1249
19,182 16,639 S2688 S1666
9,314 7,984 S2300 S2269
27,401 19,561 S336 S2909
15,380 12,775 S1980 S3063
11,844 10,613 S2295 S1479
25,753 22,437 S2249 S197
25,919 19,826 S3233 S210
15,002 13,667 S2388 S1950
9,185 7,487 S930 S2166
17,951 16,412 S244 S2262
23,305 20,678 S1902 S522

Results

The mean route length for the optimized routes for this particular sample run is 17.71 km, while the mean Euclidean desire line length is 14.74 km. This represents a percent change of 20.2% longer for the optimized routes compared to the direct desire lines. The interactive map above visualizes these routes, with desire lines colored based on their lengths and Open Street Routing Machine (OSRM) routes similarly colored with a different theme.

Discussion

The results indicate that the optimized OSRM routes are significantly longer than the direct desire lines, which is generally expected given the constraints of the built environment and road network. The percent change of 20.2% suggests that while the desire lines represent the most direct path between two points, real-world travel must navigate around obstacles, follow roadways, and adhere to traffic regulations etc.

Limitations

  • This does not represent all bus stops in NYC, just shelters. Although the exact number of bus stops is difficult to find, the MTA states that there are 327 bus routes in the five boroughs and countless stops in between. To make the data manageable both in computation and visualization, this study only selects 50 at random. This limits the amount of data points and does not fully capture the bus network.
  • The OSRM routing service may not always find a route between two points, especially if they are very close together or in areas with limited road connectivity. The code removes these unroutable routes, and they are not shown in the data.
  • The analysis does not account for real-world factors such as traffic, hazards, closures, road conditions, bus “bunching” or transit schedules, which can significantly impact actual travel times and route efficiency.The analysis assumes that the shortest path is the most efficient, which may not always be the case in real-world scenarios.
  • The sample size of 50 origin-destination pairs is relatively small and is not be representative of the entire bus network in NYC.
  • Only “Primary” and “Secondary” roads are sampled here, as the computation for the smaller roads (tertiary etc.) was too processing heavy. This eliminates a large selection of routes.

Future:

Future research could expand the sample size to include more origin-destination pairs, or even all bus stops. Incorporating real-world travel time data, traffic patterns, and transit schedules could provide a more comprehensive understanding of route efficiency. Further analysis could also explore the impact of different modes of transportation, such as cycling or walking, on route optimization and efficiency.

Additional Sources:

https://www.mta.info/agency/new-york-city-transit/subway-bus-facts-2019 https://docs.ropensci.org/stplanr/